Acta Mechanica

, Volume 226, Issue 9, pp 2831–2848 | Cite as

Application and experimental validation of new computational models of friction forces and rolling resistance

  • Grzegorz KudraEmail author
  • Jan Awrejcewicz
Open Access
Original Paper


In the process of modelling of the Celtic stone rotating and rolling on a plane surface, different versions of simplified models of contact forces between two contacting bodies are used. The considered contact models take into account coupled dry friction force and torque, as well as rolling resistance. They were developed using Padé approximations, their modifications, and polynomial functions. Before the use of these models, some kinds of regularisations have been made, allowing to avoid singularities in the differential equations. The models were tested both numerically and experimentally, giving some practical guesses of the most essential elements of contact modelling in the Celtic stone numerical simulations. Since the tested contact models do not require the space discretisation, they can find application in relatively fast numerical simulations of rigid bodies with friction contacts.


Friction Force Friction Model Contact Model Rolling Resistance Contact Pressure Distribution 
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Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Department of Automation, Biomechanics and Mechatronics (K16)Lodz University of TechnologyLodzPoland

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